Abstract This paper presents two semi-implicit nonhydrostatic models to simulate surface water waves. Both models utilize the pressure correction method to solve three-dimensional (3D) incompressible Navier–Stokes equations (NSEs), but one is a noniterative model and the other is associated with iterating to solve the Poisson equation for pressure correction terms. To meet the high computational demands, the Poisson equation is solved on the graphics processing unit (GPU) in conjunction with the conjugate gradient method. Both the accuracy in resolving the linear dispersion relation and the serially implemented efficiency of the models are assessed and discussed. Then, both models are validated with several test cases ranging from shallow to deep water. The results of the two models are very similar and show good agreement with experimental data in the shallow-water test cases. The accuracy of both models are also evaluated in deep-water nonlinear sloshing waves and 2D/3D focusing waves. In addition, the acceleration due to GPU parallelization is evaluated in a final 3D test case.

中文翻译：

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地表水波半隐式非静水力学模型的开发和评估

摘要 本文提出了两种半隐式非静水力学模型来模拟地表水波。两种模型都利用压力校正方法来求解三维 (3D) 不可压缩纳维-斯托克斯方程 (NSE)，但一种是非迭代模型，另一种与迭代求解压力校正项的泊松方程相关联。为了满足高计算需求，泊松方程在图形处理单元（GPU）上结合共轭梯度法求解。评估和讨论了解决线性色散关系的准确性和模型的串行执行效率。然后，这两个模型都通过从浅水到深水的几个测试案例进行验证。两种模型的结果非常相似，与浅水测试案例中的实验数据吻合良好。两种模型的精度也在深水非线性晃荡波和 2D/3D 聚焦波中进行了评估。此外，在最终的 3D 测试案例中评估了 GPU 并行化带来的加速。